4MA0 Higher January 2016 Paper 4 Q13
13 Here is a regular 10-sided polygon.
Diagram NOT accurately drawn
Work out the value of \(x\).
Show your working clearly.
(4)
| Scheme | Marks |
|---|---|
| \(180 - \dfrac{360}{10}\) or \(\dfrac{(10 - 2) \times 180}{10}\) or 144 oe | M1 |
| \(\dfrac{180 - \text{‘144’}}{2}\) or 18 | M1 |
| ‘144’ – 2 × ‘18’ | M1 |
| 108 | A1 |
| (4) |
Notes
M1: Unless inconsistently labelled
A1: dep on M1
Or M2 for 144 – (180 – 144)
Alternative
| Scheme | Marks |
|---|---|
| Pentagon approach – drawing in a pentagon or a statement recognising that the required angle is one of a regular pentagon | M1 |
| \(180 - \dfrac{360}{5}\) or \(\dfrac{(5 - 2) \times 180}{5}\) | M2 |
| 108 | A1 |
Notes
M1: May be implied by further work
M2: (M1 for exterior angle of pentagon as long as not seen as interior angle or given as answer)
A1: dep on M1